Hostname: page-component-5f745c7db-hj587 Total loading time: 0 Render date: 2025-01-06T07:46:31.188Z Has data issue: true hasContentIssue false
  • English
  • Français

Bayesian Item Selection Criteria for Adaptive Testing

Published online by Cambridge University Press:  01 January 2025

Wim J. van der Linden
Wim J. van der Linden*
Affiliation:
University of Twente
*
Requests for reprints should be sent to W. J. van der Linden, Department of Educational Measurement and Data Analysis, University of Twente, P.O. Box 217, 7500 AE Enschede, THE NETHERLANDS. E-mail; vanderlinden@edte.utwente.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

Owen (1975) proposed an approximate empirical Bayes procedure for item selection in computerized adaptive testing (CAT). The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity involved in a fully Bayesian approach but is no longer necessary given the computational power currently available for adaptive testing. This paper suggests several item selection criteria for adaptive testing which are all based on the use of the true posterior. Some of the statistical properties of the ability estimator produced by these criteria are discussed and empirically characterized.

Keywords

adaptive testingitem response theoryBayesian statisticsitem selection criteria
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 2 , June 1998 , pp. 201 - 216
Copyright
Copyright © 1998 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Portions of this paper were presented at the 60th annual meeting of the Psychometric Society, Minneapolis, Minnesota, June, 1995. The author is indebted to Wim M. M. Tielen for his computational support.

References

Andersen, E. B. (1980). Discrete statistical models with social science applications, Amsterdam: North-Holland.Google Scholar
Bloxom, B., & Vale, C. D. (1987, June). Multidimensional adaptive testing: An approximate procedure for updating. Paper presented at the annual meeting of the Psychometric Society, Montreal, Canada.Google Scholar
Brown, J. M., & Weiss, D. J. (1977). An adaptive testing strategy for achievement in test batteries, Minneapolis, MN: Psychometrics Program, Department of Psychology, University of Minnesota.CrossRefGoogle Scholar
Chang, H.-H., & Ying, Z. (1996). A global information approach to computerized adaptive testing. Applied Psychological Measurement, 20, 213–229.CrossRefGoogle Scholar
Gialluca, K. A., & Weiss, D. J. (1979). Efficiency of an adaptive inter-subtest branching strategy in the measurement of classroom achievement, Minneapolis, MN: Psychometrics Program, Department of Psychology, University of Minnesota.Google Scholar
Hambleton, R. K., & Swaminathan, H. (1985). Item response theory: Principles and applications, Boston: Kluwer-Nijhof.CrossRefGoogle Scholar
Kim, J. K., & Nicewander, W. A. (1993). Ability estimation for conventional tests. Psychometrika, 58, 587–599.CrossRefGoogle Scholar
Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability. Psychometrika, 48, 233–246.CrossRefGoogle Scholar
Luecht, R. M. (1995). Some alternative CAT item selection heuristics, Philadelphia, PA: National Board of Medical Examiners.Google Scholar
Owen, R. J. (1975). A Bayesian sequential procedure for quantal response in the context of adaptive testing. Journal of the American Statistical Association, 70, 351–356.CrossRefGoogle Scholar
Samejima, F. (1993). The bias function of the maximum likelihood estimate of ability for the dichotomous response level. Psychometrika, 58, 195–210.CrossRefGoogle Scholar
Schnipke, D. L., & Green, B. F. (1995). A comparison of item selection routines in linear and adaptive tests. Journal of Educational Measurement, 32, 227–242.CrossRefGoogle Scholar
Thissen, E., & Mislevy, R. J. (1990). In Wainer, H. (Eds.), Computerized adaptive testing: A primer, Hillsdale, NJ: Erlbaum.Google Scholar
van der Linden, W. J. (in press). Empirical initialization of the ability estimator in adaptive testing algorithms. Applied Psychological Measurement.Google Scholar
van der Linden, W. J., & Reese, L. M. (1998). A model for optimal constrained adaptive testing. Applied Psychological Measurement, 22.CrossRefGoogle Scholar
Veerkamp, W. J. J. (1996). Statistical inference for adaptive testing, Enschede, The Netherlands: University of Twente, Department of Educational Measurement and Data Analysis.Google Scholar
Veerkamp, W. J. J., & Berger, M. P. F. (1997). Some new item selection criteria for adaptive testing. Journal of Educational and Behavioral Statistics, 22, 203–226.CrossRefGoogle Scholar
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory with tests of finite length. Psychometrika, 54, 427–450.CrossRefGoogle Scholar
Weiss, D. J. (1982). Improving measurement quality and efficiency with adaptive testing. Applied Psychological Measurement, 4, 473–492.CrossRefGoogle Scholar
Weiss, D. J., & McBride, J. R. (1984). Bias and information of Bayesian adaptive testing. Applied Psychological Measurement, 8, 273–285.CrossRefGoogle Scholar
Wainer, H., Lewis, C., Kaplan, B., & Braswell, J. (1991). Building algebra testlets: A comparison of hierarchical and linear structures. Journal of Educational Measurement, 28, 311–323.CrossRefGoogle Scholar